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)...

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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...

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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 $...

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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...

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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 }} $ $...

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 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...

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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...

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