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A curve drawn at constant temperature is...

A curve drawn at constant temperature is called an isotherm. This shows the relationship between :

A

P and `1/V`

B

PV and V

C

V and `1/P`

D

P and V.

Text Solution

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The correct Answer is:
To solve the question regarding the relationship shown by an isotherm, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding Isotherm**: An isotherm is a curve that represents the behavior of a gas at a constant temperature. According to the ideal gas law, the relationship between pressure (P), volume (V), and temperature (T) is given by the equation PV = nRT, where n is the number of moles and R is the ideal gas constant. 2. **Applying Boyle's Law**: At constant temperature, Boyle's Law states that the pressure of a gas is inversely proportional to its volume. This means that if the volume decreases, the pressure increases, and vice versa. Mathematically, this can be expressed as: \[ P \propto \frac{1}{V} \quad \text{or} \quad PV = k \quad (\text{where } k \text{ is a constant}) \] 3. **Graphical Representation**: When we plot pressure (P) against volume (V) at constant temperature, we will get a hyperbolic curve. This curve indicates that as pressure increases, volume decreases, and as volume increases, pressure decreases. 4. **Identifying the Relationship**: From the above analysis, we can conclude that the isotherm shows the relationship between pressure (P) and volume (V) of a gas at constant temperature. 5. **Final Answer**: Therefore, the correct answer to the question is that the isotherm shows the relationship between pressure and volume.
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