A rigid vessel containing three moles of nitrogen gas at 30°C is heated to 250°C. Assume the average capacities of nitrogen to be C_p = 29.1 J/mole.°C and, C_v = 20.8 J/mole.°C. The heat required, neglecting the heat capacity of the vessel, is

ANS:B - 19206 J

To find the heat required to raise the temperature of the nitrogen gas from 30°𝐶30°C to 250°𝐶250°C, we can use the formula: 𝑄=𝑛𝐶𝑝Δ𝑇Q=nCp​ΔT Where:

• 𝑄Q is the heat required,
• 𝑛n is the number of moles of the gas,
• 𝐶𝑝Cp​ is the molar specific heat capacity at constant pressure,
• Δ𝑇ΔT is the change in temperature.

Given:

• 𝑛=3n=3 moles
• 𝐶𝑝=29.1Cp​=29.1 J/mol.°C
• Initial temperature 𝑇1=30°𝐶T1​=30°C
• Final temperature 𝑇2=250°𝐶T2​=250°C

The change in temperature Δ𝑇=𝑇2−𝑇1=250°𝐶−30°𝐶=220°𝐶ΔT=T2​−T1​=250°C−30°C=220°C Now, substitute the values into the formula: 𝑄=(3 moles)×(29.1 J/mol.°C)×(220°𝐶)Q=(3moles)×(29.1J/mol.°C)×(220°C) 𝑄=3×29.1×220Q=3×29.1×220 𝑄=19158 JQ=19158J Therefore, the heat required, neglecting the heat capacity of the vessel, is approximately 19158 J19158J. So, none of the given options match exactly, but the closest one is 19206 J19206J.