Question

If pressure of a gas is increased by $1$% when heated by $1^{\circ }C$, its initial temperature must be (if volume remains constant):

• A. $100K$
• B. ${100}^{\circ }C$
• C. $250K$
• D. ${250}^{\circ }C$

Answer 1

Answer: (A)

$100K$

Let P be the original pressure. The pressure of a gas is increased 1%. P' be the new pressure.
$P^{\prime }=\frac{100+1}{100}P=1.01P$
Let T be the original temperature (in K). Gas is heated by 1deg C. Let T' be the new temperature.
$T^{\prime }=T+1$
$\frac{P^{\prime }}{P}=\frac{T^{\prime }}{T}$
$\frac{1.01P}{P}=\frac{T+1}{T}$
$1.01=\frac{T+1}{T}$
$1.01T=T+1$
$0.01T=1$
$T=100K$
Hence, the initial temperature must be 100 K.