At a given pressure, the volume of a given amount of gas at `0^(@)C` is `V_(0)`. (i) will the V vs t (celsius temperature) plot for this gas be linear (ii) will it be a straight line passing through the origin? (iii) if this straight line does ot pass through the origin, then what will be its slope and intercept?

Explanation

(i) According to charles' law, `V_(t)=V_(0)(1+(t)/(273))`, where `V_(t) and V_(0)` are the volumes of a given mass of gas at temperature `t^(@)C` and `0^(@)C`, respectively, when the pressure of the gas is kept constant, hence the above equation can be rewritten as `V_(t)=V_(0)+(t)/(273)V_(0)` . . . [1]
`V_(0)` is a fixed quantity for a given mass of gas at a constant pressure. thus, the equation [1] represents a straight line.
(ii) Equation [1] does not represent an equation of a straight line passing through the origin. hence, `V_(t)` vs t plot will not be a straight line passing through the origin.
(iii) According to the equation [1], the straight line resulting from plot of `V_(t)` vs t has a slope of `V_(0)//273` and an intercept of `V_(0)`.