At 27^ C , one mole of an ideal gas is compressed isothermally and...

27^{\circ} \mathrm{C}

, one mole of an ideal gas is compressed isothermally and reversibly from a pressure of 2 atm to 10 atm . Choose the correct option from the following.

Options

AChange in internal energy is positive
BHeat is negative
CWork done is -965.84 cal
DAll are incorrect

Correct answer

B. Heat is negative

Step-by-step solution

Work done in isothermal reversible process is

w=-2.303 n R T \log _{10} \frac{p_1}{p_2}

Given,

\begin{aligned} n & =1, R=2 \mathrm{cal} \mathrm{K}^{-1} \mathrm{~mol}^{-1} \\ T & =(27+273) \mathrm{K}=300 \mathrm{~K} \\ p_1 & =2 \mathrm{~atm}, p_2=10 \mathrm{~atm}\end{aligned}

\begin{aligned} \therefore \quad w & =-2.303 \times 1 \times 2 \times 300 \log _{10} \frac{2}{10} \\ w & =+965.54 \mathrm{cal}\end{aligned}

For isothermal change,

\Delta U=0

Now, from first law of thermodynamics,

\begin{aligned} & q=\Delta U-W=0-965.84 \mathrm{cal} \\ & q=-965.84 \mathrm{cal}\end{aligned}

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