An ideal gas undergoes a process from state 1 (T_{1}=300 {K}, p_{1}=100 {kPa}) to state 2(T_{2}=600 {K}, p_{2}=500 {kPa}) . The specific heats of the ideal gas are: c_{\rho}=1 {kJ}{/} {kg}- {K} and C_{v}=0.7 {kJ} {/} {kg}- {K} . The change in specific entropy of the ideal gas from state 1 to state 2 (in {kJ} {/} {kg}- {K}) is (correct to two decimal places)

GATE Mechanical Engineering (ME) 2018 Shift 1 Solved Paper

Question : 12 of 65

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An ideal gas undergoes a process from state

1 \;\; (T_{1}=300 {K}, p_{1}=100 {kPa})

to state

2(T_{2}=600 {K}, p_{2}=500 {kPa}) .

The specific heats of the ideal gas are:

c_{ρ}=1 {kJ}{/} {kg}- {K}

and

C_{v}=0.7 {kJ} {/} {kg}- {K} .

The change in specific entropy of the ideal gas from state 1 to state 2

(in {kJ} {/} {kg}- {K})

is (correct to two decimal places)

Solution:

Ideal gas
State

1: T_{1}=300 {K}, P_{1}=100 {kPa}

State

2: T_{2}=600 {K}_{1} {P}_{2}=500 {kPa}

c_{p}=1 {k} {J} {/} {kg}- {K}, c_{ρ}-c_{v}=R, c_{v}=0.7 {kJ} {/} {kg}- {K}

⇒ \;\; c_{ρ}-c_{v}=1-0.7=R

R=0.3 {kJ} {/} {kg}- {K}

Change in specific entropy

s_{2}-\ov{s}_{1}=c_{ρ} \In \;{T_{2}}/{T_{1}}-R \In \;{P_{2}}/{P_{1}}

=1 × \In \;{600}/{300}-0.3 \In \;{500}/{100}

=0.21 {k}J{/}{kg}- {K}

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