If the internal energy of a thermodynamic system is increased by 300J while 75J of expansion work is done?
how much heat was transferred and in which direction to or from the system?

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The internal energy of the system is characterized by the equation U = Q + W where U is the internal energy, Q is the heat and W is work. You are given 300J of internal energy and 75J of expansion work. The heat energy is 225J.