A fixed mass of an ideal gas absorbs 1000J of heat and expands under a constant pressure of 20 kPa from a volume of 25x10(-3) m3 to a volume of 25x10(-3)m3. What is the change in internal energy of the gas?
A) -1000J
B) -900J
C) Zero
D) +500J
E) +1000J?
Need Solution
To determine the change in internal energy of the gas, we can use the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.
Knowing that the gas expands under constant pressure, the work done can be calculated using the formula: work = pressure * change in volume.
Given:
Heat (Q) = 1000J
Pressure (P) = 20 kPa = 20,000 Pa
Initial volume (V1) = 25x10^(-3) m^3
Final volume (V2) = 25x10^(-3) m^3
First, let's calculate the work done by the gas:
Change in volume (ΔV) = V2 - V1 = 25x10^(-3) m^3 - 25x10^(-3) m^3 = 0
Work (W) = Pressure * Change in volume
W = 20,000 Pa * 0
W = 0 J
Now we can find the change in internal energy (ΔU):
ΔU = Q - W
ΔU = 1000J - 0J
ΔU = 1000J
Therefore, the change in internal energy of the gas is +1000J. So the correct answer is E) +1000J.
To determine the change in internal energy of the gas, we can make use of the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.
First, let's calculate the work done by the gas. The work done during an expansion/compression of a gas at constant pressure can be calculated using the formula:
Work = Pressure * Change in Volume
Given that the pressure is constant at 20 kPa and the change in volume is 25x10^(-3) m^3 - 25x10^(-3) m^3 = 0, the work done by the gas is:
Work = 20 kPa * 0 = 0 J
Now, let's calculate the change in internal energy:
Change in Internal Energy = Heat - Work
Given that the heat added to the system is 1000 J and the work done by the system is 0 J, we have:
Change in Internal Energy = 1000 J - 0 J = 1000 J
Therefore, the change in internal energy of the gas is 1000 J.
The correct answer is:
E) +1000J