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/molelºk)
1) 200 cal
2) 400 cal
3) 100 cal
4) 250 cal​

Answer 1

200 cal energy=3/2RT then substitute the value

Answer 2

Concept:

The amount of energy needed to raise the temperature of 1 mole of gas by 1 K is known as the molar heat capacity, or C, of a gas. We need to apply the equation, Q = nCΔT

Given:

Q = 45cal

Moles of gas = 3

Rise of temperature = 5⁰C

Find:

We need to determine the heat required for 5 moles of same gas under constant pressure for a 10⁰ rise in temperature.

Solution:

A substance's heat capacity informs us of the amount of heat needed to increase a specific portion of the substance by one degree.

It is given by the formula-

Q = nCΔT where Q = heat, n = number of moles, C = molar heat capacity

At constant volume, W = 0

For heat capacity at constant volume-

Q = U = nC_vΔT

Therefore equation becomes, 45 = 3C_v (5)

45 = 15C_v

C_v = 45/15

C_v = 3

We know,

C_p = C_v + R where C_p = Heat capacity at constant pressure

C_p = 3 + 2

C_p = 5

Thus, at constant pressure,

Q = nC_pΔT

Q = 5 × 5 × 10

Q = 250 cal

Thus, the heat required for 5 moles of same gas under constant pressure for a 10⁰ rise of temperature is 250 cal.

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