Which of the following correctly describes the relationship between the volume and temperature of a fixed quantity of an ideal gas at constant pressure?
(i)V $\infty$ T
(ii)V $\infty$ 1/T
(iii)V = kT
(iv)V = k(1/T)

Question

Quizplus · Accepted Answer

The relationship between the volume and temperature of a fixed quantity of an ideal gas at constant pressure is governed by the Charles's law, which states that the volume of a gas is directly proportional to its temperature (in Kelvin), given that pressure is kept constant. Therefore, option (i) is correct. The equation can be written as V ∝ T. According to the gas equation, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. If we keep the pressure constant and rearrange the equation to express V in terms of T and other constants, we get V = (nR/P)T. This expression shows that V is directly proportional to T since n, R, and P are constant. Hence, option (iii) is also correct. Thus, the correct answer is option D (i and iii). Option (ii) is incorrect because it represents the relationship between volume and absolute temperature, not temperature alone. Option (iv) is incorrect because it proposes an inverse relationship between volume and temperature, which is inaccurate for ideal gases at constant pressure.

Which of the Following Correctly Describes the Relationship Between the Volume