Question 225: Thermodynamics & KTG

Question

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio $$\frac{V_a}{V_d}$$ and the ratio $$\frac{V_b}{V_c}$$ is:

Accepted Answer

$$\begin{aligned}
	ext { (1) } P_a V_a & =P_b V_b \quad 	ext{.... (i)}\
P_c V_c & =P_d V_d \quad 	ext{.... (ii)}
\end{aligned}$$
$$\begin{aligned}
	ext { (2) } P_a V_a^{\gamma-1} & =P_d V_d^{\gamma-1} \quad 	ext{.... (iii)}\
P_b V_b^{\gamma-1} & =P_c V_c^{\gamma-1} \quad 	ext{.... (iv)}
\end{aligned}$$
$$\begin{aligned}
& 	ext { (i) } \div 	ext { (iii) } \Rightarrow \frac{V_a}{V_a^{\gamma-1}}=\frac{P_b V_b}{P_d V_d{ }^{\gamma-1}} 	ext { (v) } \
& 	ext { (ii) } \div 	ext { (iv) } \Rightarrow \frac{V_c}{V_c^{\gamma-1}}=\frac{P_d V_d}{P_b V_b{ }^{\gamma-1}} 	ext { (vi) } \
& 	ext { (v) } 	imes 	ext { (vi) } \Rightarrow \frac{V_a}{V_a^{\gamma-1}} \frac{V_c}{V_c{ }^{\gamma-1}}=\frac{P_b V_b}{P_d V_d^{\gamma-1}} 	imes \frac{P_d V_d}{P_b V_b^{\gamma-1}} \
& \Rightarrow V_a^{\gamma-2} V_c{ }^{\gamma-2}=V_d^{\gamma-1} V_b{ }^{\gamma-2} \
& \Rightarrow \frac{V_a}{V_d}=\frac{V_b}{V_c}
\end{aligned}$$

Answer

$$\frac{V_a}{V_d} 
eq \frac{V_b}{V_c}$$

Answer

$$\frac{V_a}{V_d}=\left(\frac{V_b}{V_c}\right)^{-1}$$

Answer

$$\frac{V_a}{V_d}=\frac{V_b}{V_c}$$

Answer

$$\frac{V_a}{V_d}=\left(\frac{V_b}{V_c}\right)^2$$

Thermodynamics & KTG

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio $\frac{V_a}{V_d} and the ratio \frac{V_b}{V_c}$ is:

Choose the correct answer: