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ChemistryEdu Logo Thermodynamics | First Law of Thermodynamics#

First Law of Thermodynamics#

  • Whenever the state of a system changes, there will be change in its internal energy.
  • This change in its internal energy can be done by two ways: (a) by doing work on the system or work is done by the system (b) by supplying heat to the system or heat is released by the system.
  • This is known as First Law of Thermodynamics. It is based on energy conservation principle.
  • Mathematically, we can express first law of thermodynamics as:
\[ΔU = q + W\]

Question#

A gas contained in a cylinder fitted with a frictionless piston expands against a constant external pressure of 1 atm from volume 4 L to 14 L. In doing so, it absorbs 800 J from surrounding. Calculate the change in internal energy of the system.

\[W = - \int\limits_{V_1}^{V_2} P_{ext}dV\]

Since Pext is constant, we can write this as:

\[W = -P_{ext} (V_2 - V_1)\]
\[W = -1 (14 - 4)\]
\[W = -10\ atm L \]
\[W = -10 \times 101.3\ J\ (Since,\ 1\ atm\ L = 101.3\ J)\]
\[W = -1013\ J\]

Now, calculating ΔU from first law of thermodynamics:

\[ΔU = q + W\]
\[ΔU = 800\ J + (-1013)\ J\]
\[ΔU = -213\ J\]
  • Please note that we have used heat absorbed by the system as +800 J in the question as per sign convention.