Question

A cylinder of fixed capacity of 44.8 litres contains helium gas at STP. What is the amount of heat needed to raise the temperature of the gas in the cylinder by 15o C

Answer 1

Answer: $Q = 374 J$

Explanation:

Given that,

Temperature $\Delta t = 15^{0} C$

Volume of helium gas at STP = 44.8 litres

We know that,

The number of moles of the gas

$n = \dfrac{44.8\ litres}{22.4\ litres}$

$n = 2\ mol$

The heat energy is

$Q = n C_{v}\Delta t$

$Q = n\times 1.5R\times \Delta t$

Where, R = 8.31 J/m.K

$Q = 2\ mol\times 1.5\times 8.31\ J/m-K\times 15\ K$

$Q = 374 J$

Hence, the amount of heat needed is 374 J.

Answer 2

Answer:  373.8 J

Explanation:

At STP, one mole of Helium occupies 22.4 L volume. Thus, number of moles of Helium gas in the given cylinder:

n = (given volume)/ (volume of 1 mole at STP) = 44.8 L/22.4 L = 2 moles

mass of 2 moles of Helium = 2 × 4 g = 8 g

Temperature change = 15 K

The amount of heat required to raise the temperature of the gas at fixed volume is given by:

Q = m Cv ΔT = 8 g × 3.1156  J/g.K × 15 K =373.8 J