Question 192: Thermodynamics & KTG

Question

Two thermodynamical processes are shown in the figure. The molar heat capacity for process A and B are $$\mathrm{C}_{\mathrm{A}}$$ and $$\mathrm{C}_{\mathrm{B}}$$. The molar heat capacity at constant pressure and constant volume are represented by $$\mathrm{C_P}$$ and $$\mathrm{C_V}$$, respectively. Choose the correct statement.

Accepted Answer

For process $$\mathrm{A}$$
$$\begin{aligned}
& \log P=\gamma \log \mathrm{V} \Rightarrow \mathrm{P}=\mathrm{V}^\gamma,(\gamma>1) \
& P V^{-\gamma}=	ext { Constant }
\end{aligned}$$
$$C_A=C_V+\frac{R}{1+\gamma}$$ ..... (i)
Likewise for process $$\mathrm{B} ightarrow P V^{-1}=$$ Constant
$$\begin{aligned}
& C_B=C_v+\frac{R}{1+1} \
& C_B=C_v+\frac{R}{2} \quad 	ext{..... (ii)} \
& C_P=C_v+R \quad 	ext{..... (iii)}
\end{aligned}$$
By (i), (ii) & (iii)
$$C_P>C_B>C_A>C_v$$ [No answer matching]

Answer

$$\mathrm{C_P>C_B>C_A>C_V}$$

Answer

$$\mathrm{C}_{\mathrm{P}}>\mathrm{C}_{\mathrm{V}}>\mathrm{C}_{\mathrm{A}}=\mathrm{C}_{\mathrm{B}}$$

Answer

$$\mathrm{C}_{\mathrm{A}}=0$$ and $$\mathrm{C}_{\mathrm{B}}=\infty$$

Answer

$$\mathrm{C_A=\infty, C_B=0}$$

Thermodynamics & KTG

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