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5000J of heat are added to two moles an ideal monoatomic gas, initially at a temperature of 500K, while the gas performs 7500J of work. What is the final temperature of the gas ? (in Kelvin)
    Correct answer is '400'. Can you explain this answer?
    Verified Answer
    5000J of heat are added to two moles an ideal monoatomic gas, initiall...
    ΔU = ΔQ – ΔW = 5000 - 7500
    ΔU = –2500 J

    ⇒ ΔT = –100 K
    ⇒ T = 500 - 100 = 400 K
    The correct answer is: 400
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    Most Upvoted Answer
    5000J of heat are added to two moles an ideal monoatomic gas, initiall...
    Given:
    - Heat added to the gas (Q) = 5000 J
    - Work done by the gas (W) = 7500 J
    - Initial temperature of the gas (T₁) = 500 K
    - Number of moles of the gas (n) = 2

    Key Formulas:
    - The first law of thermodynamics states that the change in internal energy (ΔU) of a system is equal to the heat added to the system minus the work done by the system:
    ΔU = Q - W

    - For an ideal monoatomic gas, the change in internal energy is given by:
    ΔU = (3/2) nR ΔT
    where R is the gas constant and ΔT is the change in temperature.

    - The work done by the gas is given by:
    W = -PΔV
    where P is the pressure and ΔV is the change in volume.

    - For an ideal gas, the change in volume is related to the change in temperature by:
    ΔV = nR ΔT/P

    Solution:
    We can start by using the first law of thermodynamics to find the change in internal energy:
    ΔU = Q - W
    ΔU = 5000 J - 7500 J
    ΔU = -2500 J

    Since the gas is monoatomic, we can use the formula for the change in internal energy for an ideal monoatomic gas:
    ΔU = (3/2) nR ΔT
    -2500 J = (3/2) (2 mol) (8.314 J/(mol·K)) ΔT
    -2500 J = 24.942 J/K ΔT

    Simplifying the equation:
    ΔT = -100.18 K

    The negative sign indicates that the temperature has decreased. Therefore, the final temperature of the gas is:
    T₂ = T₁ + ΔT
    T₂ = 500 K - 100.18 K
    T₂ ≈ 400 K

    Therefore, the final temperature of the gas is approximately 400 K.
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    5000J of heat are added to two moles an ideal monoatomic gas, initially at a temperature of 500K, while the gas performs 7500J of work. What is the final temperature of the gas ? (in Kelvin)Correct answer is '400'. Can you explain this answer?
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