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 = 8.3 JK–1-mol–1)
To determine the amount of heat needed to raise the temperature of helium gas in a cylinder by 20.0°C, we need to use the concept of molar heat capacity at constant volume, as the gas is contained in a fixed volume. Here's how we can solve it step-by-step:
Firstly, determine the number of moles of helium gas. At Standard Temperature and Pressure (STP), 1 mole of a gas occupies 22.4 liters. Given a fixed capacity of 44.8 liters, the number of moles, n, is calculated as:
n = \frac{44.8}{22.4} = 2 \text{ moles}.
The formula to calculate the heat required at constant volume is:
Q = n \cdot C_v \cdot \Delta T,
where:
C_v is the molar heat capacity at constant volume for helium, which is 3R/2 for a monatomic ideal gas.
\Delta T is the change in temperature, given as 20°C.
Use the given gas constant R = 8.3 \, \text{JK}^{-1}\text{-mol}^{-1} to find C_v:
C_v = \frac{3}{2}R = \frac{3}{2} \cdot 8.3 = 12.45 \, \text{JK}^{-1}\text{-mol}^{-1}.
