First slide

Heat given

Question

3 moles of a monoatomic gas requires 45 cal heat for 5°C rise of temperature at constant volume, then heat required for 5 moles of same gas under constant pressure for 10°C rise of temperature is (R=2 cal/mole/°k)

Easy

A

200 cal
B

400 cal
C

100 cal
D

250 cal

Solution

n = 3 moles
for monoatiomic gas Q_V = 45cal
ΔT = $50^{0} C$
${C_V} = \frac{1}{n} \times \frac{{{Q_V}}}{{\Delta T}} = \frac{1}{3} \times \frac{{45}}{5} = 3cal/mole - k$
R = 2cal/mole–k
C_p = C_v + R = 3 + 2 = 5cal/mole - k
Now n = 5 mole, ΔT = 10°C
Q_p
${C_p} = \frac{1}{n}\frac{{{Q_p}}}{{dT}}$
$\therefore {Q_p} = n{C_p}\Delta T = 5 \times 5 \times 10 = 250cal$

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