c) using the first law of thermodynamics, write down the relation between Q, Pa, V, V0, and k. Answer: c) The relation between Q, Pa, V, V0, and k is as follows: dQ = dU + dW where, dU = Cv (T – T0)...

### Consider one mole of a perfect gas in a cylinder of unit cross-section with a piston attached. A spring is attached to the piston and to the bottom of the cylinder. Initially the spring is unstretched and the gas is in equilibrium. A certain amount of heat Q is supplied to the gas causing an increase of volume from V0 to V1.

a) what is the initial pressure of the system? b) what is the final pressure of the system? Answer: a) Pa is the initial pressure of the system inside the cylinder b) The final pressure of the...

### Consider that an ideal gas is expanding in a process given by P = f(V), which passes through a point (V0, P0). Show that the gas is absorbing heat at (P0, V0) if the slope of the curve P = f(V) is larger than the slope of the adiabat passing through (P0, V0).

Answer: The slope of the graph as given by: $ \left( {{V}_{0}},{{P}_{0}} \right)={{\left( \frac{dP}{dV} \right)}_{{{V}_{0}},{{P}_{0}}}} $ Making use of the above relation, we can determine that $...

### A cycle followed by an engine is shown in the figure. Find heat exchanged by the engine, with the surroundings for each section of the cycle considering Cv = (3/2)R.

AB: constant volume BC: constant pressure CD: adiabatic DA: constant pressure Answer: a) AB: constant volume b) BC: constant pressure c) CD: adiabatic QCD = 0 d) DA: constant pressure, there is...

### A cycle followed by an engine is shown in the figure.

A to B: volume constant B to C: adiabatic C to D: volume constant D to A: adiabatic VC = VD = 2VA = 2VB c) what is the work done by the engine in one cycle in terms of PA, PB, VA? d) what is the...

### A cycle followed by an engine is shown in the figure.

A to B: volume constant B to C: adiabatic C to D: volume constant D to A: adiabatic VC = VD = 2VA = 2VB a) in which part of the cycle heat is supplied to the engine from outside? b) in which part of...

### Consider a P-V diagram in which the path followed by one mole of a perfect gas in a cylindrical container is shown in the figure.

c) given the internal energy for one mole of gas at temperature T is (3/2)RT, find the heat supplied to the gas when it is taken from state 1 to 2 with V2 = 2V1. Answer: We know that the expression...

### Consider a P-V diagram in which the path followed by one mole of a perfect gas in a cylindrical container is shown in the figure.

a) find the work done when the gas is taken from state 1 to state 2 b) what is the ratio of temperature T1/T2 if V2 = 2V1 Answer: According to the question, PV1/2 = K = constant a) Expression for...

### The initial state of a certain gas is Pi, Vi, Ti. It undergoes expansion till its volume becomes Vf. Consider the following two cases:

a) the expansion takes place at constant temperature b) the expansion takes place at constant pressure Plot the P-V diagram for each case. In which of the two cases, is the work done by the gas...

### If the coefficient of performance of a refrigerator is 5 and operates at the room temperature, find the temperature inside the refrigerator.

Answer: To determine the temperature inside the refrigerator, we must first determine the work that has been done. W = 0 Q1 = Q2 β = ∞ Where β represents the coefficient of performance According to...

### In a refrigerator, one removes heat from a lower temperature and deposits to the surroundings at a higher temperature. In this process, mechanical work has to be done, which is provided by an electric motor. If the motor is of 1kW power, and heat is transferred from -3oC to 27oC, find the heat taken out of the refrigerator per second assuming its efficiency is 50% of a perfect engine.

Answer: Expression for the efficiency of the Carnot engine is as follows; $ \eta =1-\frac{{{T}_{2}}}{{{T}_{1}}} $ Where T1 = 300 K and T2 = 270 K We are given that the efficiency is 50% = 0.5...

### Consider a cycle tyre being filled with air by a pump. Let V be the volume of the tyre and at each stroke of the pump ∆V of air is transferred to the tube adiabatically. What is the work done when the pressure in the tube is increased from P1 to P2?

Answer: The equation before and after the stroke can be written as follows: $ {{P}_{1}}{{V}_{1}}={{P}_{2}}V_{2}^{\gamma } $ $ P{{\left( V+\Delta V \right)}^{\gamma }}=(P+\Delta P){{V}^{\gamma }} $ $...

### A person of mass 60 kg wants to lose 5 kg by going up and down a 10 m high stairs. Assume he burns twice as much fat while going up than coming down. If 1 kg of fat is burnt on expending 7000 kilocalories, how many times must he go up and down to reduce his weight by 5 kg?

Answer: According to the question, the height of the stairs is h = 10 m And the work done to burn 5 kg of fat is W = (5)(7000 × 103)(4.2) W = 147 × 106 J Therefore, the work done towards burning of...

### Consider a Carnot’s cycle operating between T1 = 500K and T2 = 300K producing 1 kJ of mechanical work per cycle. Find the heat transferred to the engine by the reservoirs.

Answer: According to the question, the temperature of the source is T1 = 500 K and the temperature of the sink is T2 = 300 K We also have the work done per cycle as W = 1 kJ = 1000 J we have to...

### Air pressure in a car tyre increases during driving. Explain.

Answer: According to Charle's law, the air pressure in a car tyre increases while the volume remains constant during driving. Temperature and pressure are proportional. As a result, the pressure of...

### Is it possible to increase the temperature of a gas without adding heat to it? Explain.

Yes, it is possible to raise a gas's temperature without adding heat to it. During adiabatic compression, this is feasible. In adiabatic compression, we know that dQ=0 ∴ Making use of the first law...

### If a refrigerator’s door is kept open, will the room becomes cool or hot? Explain.

Answer: When a refrigerator door is left open, the room becomes hot because the quantity of heat received by the refrigerator, as well as the work performed by the refrigerator, is rejected into the...

### A system goes from P to Q by two different paths in the P-V diagram as shown in the figure. Heat given to the system in the path 1 is 1000 J. The work done by the system along path 1 is more than path 2 by 100 J. What is the heat exchanged by the system in path 2?

Answer: From path 1 we can say that, Q1 = +1000 J and the work done is W1 – W2 = 100 Where W1 represents the work done through path 1 and W2 denotes the work done through path 2. Therefore, we can...

### Can a system be heated and its temperature remains constant?

Answer: Yes, if the complete amount of heat provided to the system is used for expansion. To maintain a constant temperature, the system's work against the environment should be compensated by the...

### Consider a heat engine as shown on the figure. Q1 and Q2 are heat added to heat bath T1 and heat taken from T2 in one cycle of the engine. W is the mechanical work done on the engine.

If W > 0, then possibilities are: a) Q1 > Q2 > 0 b) Q2 > Q1 > 0 c) Q2 < Q1 < 0 d) Q1 < 0, Q2 > 0 Answer: The correct options are a) Q1 > Q2 > 0 c) Q2 < Q1 < 0...

### Consider a cycle followed by an engine

1 to 2 is isothermal 2 to 3 is adiabatic 3 to 1 is adiabatic Such a process does not exist because a) heat is completely converted to mechanical energy in such a process, which is not possible b)...

### Figure shows the P-V diagram of an ideal gas undergoing a change of state from A to B. Four different parts I, II, III, and IV as shown in the figure may lead to the same changes of state.

a) change in internal energy is the same in IV and III cases, but not in I and II b) change in internal energy same in all the four cases c) work done is maximum in case I d) work done is minimum in...

### An ideal gas undergoes isothermal process from some initial state I to final state f. Choose the correct alternatives

a) dU = 0 b) dQ = 0 c) dQ = dU d) dQ = dW Answer: The correct options are a) dU = 0 d) dQ = dW Explanation: Internal energy is a function of temperature. Since temperature is constant...

### Which of the process described below are irreversible?

a) the increase in temperature of an iron rod by hammering it b) a gas in a small container at a temperature T1 is brought in contact with a big reservoir at a higher temperature T2 which increases...

### Three copper blocks of masses M1, M2, and M3 kg respectively are brought into thermal contact till they reach equilibrium. Before contact, they were at T1, T2, T3 (T1 > T2 > T3). Assuming there is no heat loss to the surroundings, the equilibrium temperature T is

a) b) c) d) Answer: The correct option is b)

### Consider two containers A and B containing identical gases at the same pressure, volume, and temperature. The gas in container A is compressed to half of its volume isothermally while the gas in the container B is compressed to half of its original value adiabatically. The ratio of final pressure of a gas in B to that of gas in A is

Answer: The correct answer is a)

### An ideal gas undergoes cyclic process ABCDA as shown in the given P-V diagram. The amount of work done by the gas is

a) 6P0V0 b) -2P0V0 c) +2P0V0 d) +4P0V0 Answer: The correct option is d) +4P0V0 Explanation Work done by the gas is equal to the area of rectangle ABCDA =AB×BC =(2V0)P0 =2P0V0 This work is done on...

### Consider P-V diagram for an ideal gas shown in the figure.

Out of the following diagrams, which represent the T-P diagram? a) iv b) ii c) iii d) i Answer: The correct option is c) iii Explanation: In the above-mentioned graph, PV=constant Moreover, PV=nRT...

### If an average person jogs, he produces 14.5 × 103 cal/min. This is removed by the evaporation of sweat. The amount of sweat evaporated per minute is assuming 1 kg requires 580 × 103 cal for evaporation

a) 0.25 kg b) 2.25 kg c) 0.05 kg d) 0.20 kg Answer: The correct option is a) 0.25 kg Explanation: Energy produces = 14.5 × 103 cal/min. Then the amount of sweat evaporated per min is given...

### An ideal gas undergoes four different processes from the same initial state. Four processes are adiabatic, isothermal, isobaric, and isochoric. Out of 1, 2, 3, and 4 which one is

a) 4 b) 3 c) 2 d) 1 Answer: The correct option is c) 2 Explanation: The adiabatic process occurs when a thermodynamic system changes in such a way that no heat exchange occurs between it and its...