This cylinder is fitted with a light, movable piston. Fig. 1 shows a student heating the trapped gas slowly. A load of 400 N acts on a piston of area 0.0020...
Question 1 Report
This cylinder is fitted with a light, movable piston. Fig. 1 shows a student heating the trapped gas slowly. A load of 400 N acts on a piston of area 0.0020 m2. Atmospheric pressure outside the cylinder is 100 kPa. Initially the gas volume is 0.50 L at 290 K. The piston can move freely, so the gas pressure remains constant while it is heated to 350 K.
(a) State the SI unit of pressure. [1]
(b) Calculate the pressure exerted by the 400 N load on the piston. [3]
(c) Calculate the absolute pressure of the gas in the cylinder. [3]
(d) Calculate the final volume of the gas at 350 K. [2]
(e) Explain why the piston moves upwards as the gas is heated. [2]
Answer Details
(a) The SI unit of pressure is the pascal, Pa. [1]
(b)
\[p=\frac{F}{A}=\frac{400}{0.0020}=2.0\times10^5\text{ Pa}\]
\[=200\text{ kPa}\]
The load exerts \(2.0\times10^5\text{ Pa}\), or 200 kPa. [3]
(c) The gas balances both the load pressure and atmospheric pressure:
\[p_{\text{gas}}=200\text{ kPa}+100\text{ kPa}=300\text{ kPa}\]
The absolute gas pressure is 300 kPa. [3]
(d) Pressure remains constant, so \(V/T\) is constant:
\[V_2=0.50\times\frac{350}{290}=0.603\text{ L}\]
The final volume is 0.60 L. [2]
(e) Heating gives the molecules more kinetic energy. The gas expands and pushes the piston upward until its pressure balances the external pressure. [2]
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