Pressure, volume and temperature relationships
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Question
State Boyle's law.
Answer
At **constant temperature**, the pressure and volume of a fixed mass of gas obey **P V = constant** (inversely proportional).
Question
State Charles' law.
Answer
At **constant pressure**, the volume of a fixed mass of gas obeys **V ÷ T = constant** — volume is proportional to the absolute (kelvin) temperature.
Question
State Gay-Lussac's law.
Answer
At **constant volume**, the pressure of a fixed mass of gas obeys **P ÷ T = constant** — pressure is proportional to the absolute (kelvin) temperature.
Question
What is the combined gas law?
Answer
$\dfrac{PV}{T} = \text{constant}$ — so $\dfrac{P_1 V_1}{T_1} = \dfrac{P_2 V_2}{T_2}$. **Given** in the data booklet.
Question
How do you convert °C to kelvin?
Answer
**T (K) = θ (°C) + 273.** Always do this before using a gas law.
Question
Why must temperature be in kelvin for gas laws?
Answer
The laws count temperature from **absolute zero** (−273 °C = 0 K); only the kelvin scale makes V and P truly proportional to T.
Question
Shape of a pressure–volume (P–V) graph at fixed temperature?
Answer
A **curve** (hyperbola) that sweeps down to the right, because P V is constant.
Question
Shape of a graph of P against 1/V at fixed temperature?
Answer
A **straight line through the origin**, because P = K(1/V); its **slope is the constant K**.
Question
What is the SI unit of the Boyle constant K (= P V)?
Answer
Pressure × volume = **Pa × m³ = J** (the joule).
Question
Sealed rigid can is heated — what happens to the pressure?
Answer
Volume is fixed, so **P ÷ T = constant**: the pressure rises in proportion to the kelvin temperature.
Question
Most common gas-law mistake?
Answer
Leaving the temperature in **°C** — every gas-law T must be in **kelvin** (°C + 273).
Question
Each single law is a special case of which equation?
Answer
The **combined gas law** P V ÷ T = constant: fix T → Boyle, fix P → Charles, fix V → Gay-Lussac.
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