Thermodynamics

### 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.

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...

### 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)

### 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...