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(B) For an isothermal process, the work done is given by $W_{	ext{isothermal}} = nRT \ln \left(\frac{V_2}{V_1}ight)$.Given $n = 1$, $T = 27^{\circ}

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$-56$

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(B) For an isothermal process, the work done is given by $W_{	ext{isothermal}} = nRT \ln \left(\frac{V_2}{V_1}ight)$.Given $n = 1$, $T = 27^{\circ} C = 300 \ K$, and $V_2/V_1 = 2$, we have $W = 1 \cdot R \cdot 300 \cdot \ln(2) \approx 300R(0.693)$.For an adiabatic process, the work done is $W_{	ext{adiabatic}} = \frac{nR(T_1 - T_2)}{\gamma - 1}$.For a diatomic gas, $\gamma = 1.4$.Given $W_{	ext{isothermal}} = W_{	ext{adiabatic}}$, we equate the two expressions:$\frac{1 \cdot R(300 - T_{	ext{final}})}{1.4 - 1} = 300R(0.693)$.$\frac{300 - T_{	ext{final}}}{0.4} = 300(0.693)$.$300 - T_{	ext{final}} = 0.4 \cdot 300 \cdot 0.693 = 83.16$.$T_{	ext{final}} = 300 - 83.16 = 216.84 \ K$.Converting to Celsius: $T(^{\circ} C) = 216.84 - 273.15 \approx -56.31^{\circ} C$.Thus, the final temperature is close to $-56^{\circ} C$.

List-$I$	List-$II$
$(a)$ Isothermal	$(i)$ Pressure constant
$(b)$ Isochoric	$(ii)$ Temperature constant
$(c)$ Adiabatic	$(iii)$ Volume constant
$(d)$ Isobaric	$(iv)$ Heat content is constant

Similar Questions

Match List-$I$ with List-$II$:

List-$I$ List-$II$

$(a)$ Isothermal $(i)$ Pressure constant

$(b)$ Isochoric $(ii)$ Temperature constant

$(c)$ Adiabatic $(iii)$ Volume constant

$(d)$ Isobaric $(iv)$ Heat content is constant

Choose the correct answer from the options given below:

$A$ gas follows $VT^2 = \text{constant}$. The coefficient of volume expansion of the gas is

An ideal monoatomic gas expands to twice its volume. If the process is isothermal,the magnitude of work done by the gas is $W_i$. If the process is adiabatic,the magnitude of work done by the gas is $W_a$. Which of the following is true?

The following figure shows the $P-T$ graph for four processes $A, B, C,$ and $D$. Select the correct alternative.

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