A process takes place at constant pressure. The volume changes and the temperature increases by 91.0oC. The heat capacity of the system at constant volume, CV, is 695.6 kJ/oC. What is ΔE in kJ? (Careful--pay attention to the units of the heat capacity.)
To find the change in energy (ΔE) in this process, we can use the equation:
ΔE = n * CV * ΔT
where:
n is the number of moles of the substance involved
CV is the heat capacity at constant volume
ΔT is the change in temperature
In this case, we are not given the number of moles of the substance involved. However, since the process takes place at constant pressure, we can assume it is an ideal gas and use the ideal gas law to find the number of moles.
The ideal gas law equation is:
PV = nRT
where:
P is the pressure
V is the volume
n is the number of moles
R is the ideal gas constant
T is the temperature
Since the process takes place at constant pressure, the equation simplifies to:
V = nRT/P
We are not given the pressure, so we cannot calculate the number of moles using the ideal gas law directly. However, since the process is at constant pressure, the change in volume is directly proportional to the change in temperature. So we can express the change in volume (ΔV) in terms of the initial volume (V) and the change in temperature (ΔT) as:
ΔV = V * (ΔT / T)
Using the given information, we can substitute the values in the equation:
ΔV = V * (91.0oC / T)
Now, we can substitute this expression for ΔV into the ideal gas law equation:
V * (91.0oC / T) = nRT/P
Simplifying, we get:
n = V * (91.0oC / T) * P / RT
Now we have the number of moles (n). We can substitute this value into the equation for ΔE:
ΔE = n * CV * ΔT
Substituting the given values:
ΔE = [(V * (91.0oC / T) * P / RT)] * 695.6 kJ/oC * 91.0oC
After simplifying, you can calculate ΔE in kJ.