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24 August, 20:28

Two containers are bought in thermal contact. Container 1 held a liquid with specific heat 4.03 kJ/kg K at a temperature of 306 K. Container 2 held another liquid with specific heat 3.51 kJ/kg K at a temperature of 173 K. If these 2 containers held the same mass of liquid, what is the temperature once thermal equilibrium is reached?

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  1. 24 August, 21:14
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    The temperature once the thermal equilibrium is reached is 244.1 Kelvin

    Explanation:

    Step 1: Data given

    Container 1 has a liquid with specific heat = 4.03 kJ/kg*K

    this liquid is at a temperature of 306 K

    Container 2 has a liquid with specific heat = 3.51 kJ/kg*K

    this liquid is at a temperature of 173 K

    Step 2: Calculate the temperature at equilibrium

    ΔU1 + ΔU2 = 0

    Q1 + Q2 = 0

    m1*c1 * (T-T1) = - m2*c2 * (T-T2)

    ⇒ with m1 = m2

    ⇒ with c1 = the specific heat of liquid 1 = 4.03 kJ/kg*K

    ⇒ with T1 = 306 K

    ⇒ with m2 = m1

    ⇒ with c2 = the specific heat of liquid 2

    ⇒ with T1 = 173 K

    Since m1 = m2 we can write this formula as followed:

    c1 * (T-T1) = - c2 * (T-T2)

    4.03 kJ/kg*K * (T - 306K) = - 3.51 kJ/kg*K * (T-173K)

    4.03 T - 1233.18 = - 3.51 T + 607.23

    7.54 T = 1840.41

    T = 244.1 K

    The temperature once the thermal equilibrium is reached is 244.1 Kelvin
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