Cylinder contains 250 g of helium at 200 k. the external pressure is constant at 1 atm. the temperature of the surroundings is lowered by 97 k. calculate the heat lost or gained by the system in response to this change in the external temperature. express your answer in j. heat capacity for helium = 20.8 j/(mol k) molecular weight for helium = 4 g/mol

The system gains 126100 J

Explanation:

The heat can be calculated by the equation:

Q = nxCxΔT, where Q is the heat, C is the heat capacity,n is the number of moles and ΔT is the variation of temperature (final - initial). The number of moles is the mass divided by the molar mass, so:

n = 250/4 = 62.5 mol.

The system must be in thermal equilibrium with the surroundings, so if the temperature of the surroundings decreased 97 K, the temperature of the system increased by 97 K, so ΔT = 97 K

Q = 62.5x20.8x97

Q = 126100 J

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