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What are some examples of a thermodynamic system where no work is done on the system, but the first law is applied?

Work in thermodynamics is based around volume. Would that mean if the system's volume decreased, then work is done by the system instead of on the system?

As an example: If heat is applied to ice and it melts, it's volume will decrease. Despite heat being added to the system does the decreased volume mean work was not done on the system?

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  • $\begingroup$ If the volume decreases, then the system was compressed. This means that positive compression work was done on the system, and so part of the change in internal energy of the system is due to energy flowing in via work. An example of where no work is done is heating of an ideal gas in a rigid container. $\endgroup$
    – march
    Commented Mar 5, 2016 at 18:14

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Water freezing is unlike most substances, most metals contract slightly when they solidify.

The first law of thermodynamics is simply a statement of the conservation of energy: if I apply force to a cylinder of gas, such as happens in a diesel engine. The work done = the integral of (force * distance) is converted to heat, which raises the temperature of the gas, which in the case of a Diesel engine becomes hot enough to ignite the fuel, repeating the process.

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We can apply this situation where the volume remains constant ie $p\delta v=0$ as $v_2-v_1=0$ that is any isochoric process.

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