Question

A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by 20.0°C will be : (Given: gas constant R = 8.3JK^-1 moI^-1)

विकल्प

• 249 J

• 415 J

• 498 J

• 830 J

Answer 1

498 J

Explanation:

As the cylinder is of fixed capacity it means its volume is fixed.

Hence, it is an Isochoric process.

Helium is at S.T.P. conditions (given).

By Avogadro Hypothesis, one mole of gas occupies 22.4 L volume at S.T.P. condition.

⇒ Thus, at S.T.P. 44.8 L volume will be occupied by 2 moles of Helium Gas.

⇒ As, Helium is monoatomic gas, its degree of freedom will be 3.

For Isochoric Process

Q = ΔU where Q is the heat transfer ΔU ⇒ change in internal energy of gas ΔU = nC_VΔT wgere C_V is specific heat at constant volume 

⇒ C_V = `fR/2 3R/2` = for monoatomic gas   ...(where, f = degree of freedom)

Given: ΔT = 20°C

Thus, Q = ΔU = 2 × 3/2 R × 20 = 60 R

⇒ Q = 60 × 8.3 = 498 J.