NCERT Solutions for Chapter: Thermodynamics, Exercise 5: LA

A cycle followed by an engine (made of one mole of perfect gas in a cylinder with a piston) is shown in Figure. A to B volume is constant, B to C adiabatic, C to D: volume is constant D to A  adiabatic. $V_C=V_D=2V_A=2V_B$

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

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

A to B :volume constant

B to C: adiabatic

C to D: volume constant
D to A : adiabatic
$V_C=V_D=2V_A=2V_B$

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

A cycle followed by an engine (made of one mole of perfect gas in a cylinder with a piston) is shown in Figure. A to B volume is constant. B to C, the process is adiabatic, C to D volume constant
D to A is adiabatic. Also, $V_C=V_D=2V_A=2V_B$.

What is the work done by the engine in one cycle? Write your answer in terms of $P_A,P_B,V_A?$ Given: $\gamma =\frac{5}{3}$ for the gas.

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

A to B :volume constant

B to C: adiabatic

C to D: volume constant
D to A : adiabatic
$V_C=V_D=2V_A=2V_B$

 What is the efficiency of the engine?
$\left.\gamma =\frac{5}{3} \mathrm{for} \mathrm{the}gas\right]·\left[C_v=\frac{3}{2}R \mathrm{for} \mathrm{one}mole\right]$

 A cycle followed by an engine (made of one mole of an ideal gas in a cylinder with a piston) is shown in the figure below.

Find the heat exchanged by the engine, with the surroundings for each section of the cycle. $\left(C_v=\frac{3}{2}R\right)$
(a) AB: constant volume
(b) BC: constant pressure
(c) CD: adiabatic

(d) DA: Constant pressure

Consider one mole of perfect gas in a cylinder of unit cross section with a piston attached (Figure). 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 ${\mathrm{V}}_{\mathrm{o}}$ to ${\mathrm{V}}_1$.

What is the initial pressure of the system?

Consider one mole of a perfect gas in a cylinder of unit cross-section with a piston attached (Figure). 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 ${\mathrm{V}}_{\mathrm{o}}$ to ${\mathrm{V}}_1$.

 What is the final pressure of the system?

Consider one mole of perfect gas in a cylinder of unit cross-section with a piston attached (Figure). 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 ${\mathrm{V}}_{\mathrm{o}}$ to ${\mathrm{V}}_1$.

 Using the first law of thermodynamics, write down a relation between $Q,P_a,V_1,V_0$and $k$