Question

Charles's law is represented mathematically as ___________.

(symbols have their usual meanings)

• A. $V_t=K{V}_{o}t$
• B. $V_A=\frac{K{V}_o}{t}$
• C. $V_t=V_o(1+\frac{273}{t})$
• D. $V_t=V_o(1+\frac{t}{273})$

Answer 1

The correct option is D $V_t=V_o(1+\frac{t}{273})$

According to Charles's law, at a given pressure, for a given mass of a gas, the volume of a dry gas is proportional to its absolute temperature.

This means that, $V_t=xT$, where $x$ is a constant.

Now, at $T=273K$, let $V=V_o$.

So, $V_o=x273$

$⟹x=\frac{V_o}{273}$

Now, putting this in the equation: $V_t=xT$, we get, $V_t=\frac{V_o}{273}T$.

Now, let $t$ be the temperature in celsius.

So, $T=273+t$

Putting this again, we get

$V_t=\frac{V_o}{273}(t+273)=V_o(1+\frac{t}{273})$