First slide

Heat given

Question

Four moles of a perfect gas heated to increase its temperature by 2°C absorbs heat of 40 cal at constant volume. If the same gas is heated at constant pressure the amount of heat supplied is, (R=2 cal/mol K)

Easy

A

28 cal
B

56 cal
C

84 cal
D

94 cal

Solution

$\Delta {Q_v} = du = n{c_v}\Delta T \Rightarrow 40 = 4 \times {c_v} \times 2$
$\therefore {c_v} = 5cal/mol\,K$
$\therefore {c_p} - {c_v} = R$
$\therefore {c_p} = {c_v} + R$
$\therefore {c_p} = 5 + 2 = 7\,cal/mol\,K$
$\Delta {Q_p} = n{c_p}\Delta T = 4 \times 7 \times 2 = 56\,cal$

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