Assume the gas is diatomic, calculate how much heat was added to the gas in the process.
One mole of ideal gas initially at a temperature of Ti=0 Celsius undergoes an expansion at a constant pressure of 1.00 atm four times its orginal volume
To calculate the amount of heat added to a diatomic gas during an expansion, we need to use the specific heat capacity at constant volume (Cv) and the Ideal Gas Law.
Given:
- Initial temperature (Ti) = 0 °C = 273.15 K
- Initial volume (Vi) = V
- Final volume (Vf) = 4V
- Pressure (P) = 1.00 atm
Step 1: Convert the initial temperature to Kelvin.
Ti(K) = Ti(°C) + 273.15
= 0 + 273.15
= 273.15 K
Step 2: Calculate the change in volume.
ΔV = Vf - Vi
= (4V) - V
= 3V
Step 3: Calculate the work done by the gas during expansion.
Remember that work done by a gas is given by:
W = -PΔV
= -(1.00 atm) * (3V) * (101.325 J)
= -303.975 J
Step 4: Calculate the amount of heat added.
From the First Law of Thermodynamics, we have:
ΔQ = ΔU + W
Since it's an expansion at constant pressure, ΔU = Cv * ΔT, where ΔT is the change in temperature.
Thus, ΔQ = Cv * ΔT + W
However, to calculate ΔQ, we need to know the specific heat capacity at constant volume (Cv) of the gas. Since it is not given in the question, we cannot determine the exact amount of heat added without this information.
If you have the value of Cv for the diatomic gas in question, you can replace Cv in the equation with its specific value and calculate ΔQ using the given formulas.