Consider a system in which 3.60 mol of an ideal monatomic gas is expanded at a constant pressure of 101 kPa from an initial volume of 2.15 L to a final volume of 3.87 L.
(b) Find the change in temperature for this process.
? K
(c) Determine the amount of heat added to or removed from the system during this process.
? J
(b) Since the pressure is constant, T is proportional to V in this process. Use the ideal gas law to get the initial temperature.
(c) Heat added = Internal energy change + work done
= (3/2)R(delta T)*n + P *delta V
To find the change in temperature for this process, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in pascals)
V = volume (in cubic meters)
n = number of moles of gas
R = gas constant (8.314 J/(mol·K))
T = temperature (in kelvin)
Since the pressure and number of moles of gas remain constant in this process, we can rewrite the equation as:
V/T = constant
To find the change in temperature, we can set up the equation as follows:
(V1 / T1) = (V2 / T2)
V1 and T1 represent the initial volume and temperature, and V2 and T2 represent the final volume and temperature, respectively.
Given:
P = 101 kPa = 101,000 Pa
V1 = 2.15 L = 0.00215 m^3
V2 = 3.87 L = 0.00387 m^3
n = 3.60 mol
R = 8.314 J/(mol·K)
Now let's solve for T2:
(T2 / T1) = (V2 / V1)
T2 = (V2 / V1) * T1
Substituting the given values:
T2 = (0.00387 m^3 / 0.00215 m^3) * T1
T2 = (1.8000) * T1
Since the change in temperature is T2 - T1, we can find the change in temperature by subtracting T1 from both sides of the equation:
T2 - T1 = (1.8000) * T1 - T1
T2 - T1 = 0.8000 * T1
Now, we know that T2 - T1 = ΔT (change in temperature). Let's solve for ΔT:
ΔT = 0.8000 * T1
To determine T1, we need to find the initial temperature of the gas. Unfortunately, the given information does not provide the initial temperature. Without the initial temperature, we cannot calculate the exact change in temperature using the given information.
Moving on to part (c) of the question, to determine the amount of heat added to or removed from the system during this process, we would need the specific heat capacity of the gas or the heat capacity at constant pressure (Cp) value. However, this information is not provided in the given question. Therefore, we cannot calculate the amount of heat added or removed without that specific information.