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  1. Problems
  2. /Find Δ U for a gas in each case, and say whether it gets warmer or cooler…
EasyPhysicsHigh School (11–12)Heat & Thermodynamics › Laws of ThermodynamicsNumericalBoard ExamAPA-LevelIB

Find Δ U for a gas in each case, and say whether it gets warmer or cooler…

StemPy LabContributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Find ΔU\Delta UΔU for a gas in each case, and say whether it gets warmer or cooler.

  1. Q=+650 JQ = +650\ \text{J}Q=+650 J, W=+240 JW = +240\ \text{J}W=+240 J.
  2. Q=−155 JQ = -155\ \text{J}Q=−155 J, W=+115 JW = +115\ \text{J}W=+115 J.
  3. Q=0Q = 0Q=0, W=−170 JW = -170\ \text{J}W=−170 J.
  4. Q=+280 JQ = +280\ \text{J}Q=+280 J, W=0W = 0W=0.

Check your answer

Work it out on paper, then type your number. The answer itself stays hidden.

J
J
J
J
Need a reminder? The key ideaShowHide

The first law: ΔU=Q−W\Delta U = Q - WΔU=Q−W. QQQ is positive when heat goes into the gas; WWW is positive when the gas does work on its surroundings, so work done on the gas is negative. For an ideal gas, ΔU>0\Delta U > 0ΔU>0 means it gets warmer.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

Step 1. (a) 650 J−240 J=+410 J650\ \text{J} - 240\ \text{J} = +410\ \text{J}650 J−240 J=+410 J: warmer.

Step 2. (b) −155 J−115 J=−270 J-155\ \text{J} - 115\ \text{J} = -270\ \text{J}−155 J−115 J=−270 J: cooler. It loses heat and does work.

Step 3. (c) 0−(−170)=+170 J0 - (-170) = +170\ \text{J}0−(−170)=+170 J: warmer, squeezed with no heat out.

Step 4. (d) 280 J−0 J=+280 J280\ \text{J} - 0\ \text{J} = +280\ \text{J}280 J−0 J=+280 J: warmer, heated in a rigid tank.

Answer: (a) +410 J+410\ \text{J}+410 J, (b) −270 J-270\ \text{J}−270 J, (c) +170 J+170\ \text{J}+170 J, (d) +280 J+280\ \text{J}+280 J.

Watch out. Subtracting a negative WWW adds it.

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