Question

A cylinder of fixed capacity of 44.8 liters 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 = 8.3 JK⁻¹-moI⁻¹)

(A) 249 J

(B) 415 J

(C) 498 J

(D) 830 J

Answer 1

To calculate the heat needed to raise the temperature of the helium gas by 20.0°C, we use the specific heat formula for monatomic gases in conjunction with the number of moles at STP. Upon calculation, we determine that the amount of heat required is 498 J.

Step-by-step explanation:

The student is asking about the amount of heat needed to raise the temperature of a certain volume of helium gas by 20.0°C, given the gas constant and the fact that the cylinder is at standard temperature and pressure (STP). To find the amount of heat ({Q}), we use the formula for a monatomic gas: {Q = (3/2)nRTΔT}, where {n} is the number of moles, {R} is the universal gas constant, and ΔT is the change in temperature.

First, we have to find the number of moles of helium using the ideal gas law ({PV = nRT}). At STP, the volume ({V}) is 44.8 liters and pressure ({P}) is 1 atm.

Since 1 mol of an ideal gas at STP occupies 22.4 L, the number of moles of helium is 2 ({44.8 L / 22.4 L/mol}). Now applying the heat formula: {Q = (3/2) * 2 moles * 8.3 J/K·mol * 20.0 K = 498 J}. Therefore, the amount of heat needed is 498 J.