# NCERT Class 11 Physics Chapter 12 Thermodynamics CBSE Board Sample Problems

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**Question 24:**

A cycle followed by an engine (made of one mole of perfect gas in a cylinder with a piston) is shown in Fig. 12.10.

A to B: volume constant

B to C: adiabatic

C to D: volume constant

D to A: adiabatic

(a) In which part of the cycle heat is supplied to the engine from outside?

(b) In which part of the cycle heat is being given to the surrounding by the engine?

(c) What is the work done by the engine in one cycle? Write your answer in term of *PA*, *PB*, *VA*.

(d) What is the efficiency of the engine?

**Answer:**

(a) A to B

(b) C to D

(c)

Similarly.

Similarly.

Now

Similarly,

Total work done

(d) Heat supplied during process A, B

**Question 25:**

A cycle followed by an engine (made of one mole of an ideal gas in a cylinder with a piston) is shown in Fig. 12.11. Find heat exchanged by the engine, with the surroundings for each section of the cycle

AB: constant volume

BC: constant pressure

CD: adiabatic

DA: constant pressure

**Answer:**

**Question 26:**

Consider that an ideal gas (*n* moles) 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 adiabatic passing through (*P0, V0* ).

**Answer:**

Slope of

Slope of adiabatic at

Now heat absorbed in the process

Since

Thus

Heat is absorbed when when gas expands, that is when

**Question 27:**

Consider one mole of perfect gas in a cylinder of unit cross section with a piston attached (Fig. 12.12). A spring (spring constant *k*) is attached (unstretched length *L*) 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 to .

(a) What is the initial pressure of the system?

(b) What is the final pressure of the system?

(c) Using the first law of thermodynamics, write down a relation between and *k*.

**Answer:**

(a)

(b)

(c) All the supplied heat is converted to mechanical energy. No change in internal energy (Perfect gas)

Where