the temperature & the pressureThe pressure in a constant-volume gas thermometer is 0.700 atm at 100 Celsius degree and 0.512 atm at 0 Celsius...

As the mass and volume of the gas in the thermometer is
constant, the change in pressure of the gas is directly proportional to the rise of
temperature. Stated in other words rise in pressure per degree rise in temperature is
constant.

Given:

Pressure at
100 degrees Celsius = 0.700 atm

Pressure at 0 degrees
Celsius = 0.512
atm

Therefore:

Rise in
pressure for 100 degrees rise in temperature = 0.700 0.512 = 0.188
atm

Therefore:

Rise in
temperature per degree Celsius rise in temperature = 0.188/100 = 0.00188
atm

Therefore:

Temperature in
Celsius corresponding to any pressure p is equal to:

t = (p
- p0)/(rise in pressure per degree Celsius temperature)

=
(p - 0.512)/0.00188

Therefore temperature corresponding to
pressure of 0.040:

= (0.040 - 0.512)/).00188 -
0.112/0.00188 = 59.57 degree Celsius.

Similarly, pressure p
in atm at any given temperature t is given by:

p = p0 +
t*(Rise in temperature per degree Celsius rise in
temperature)

= 0.512 +
t*0.00188

Therefore the pressure at 450 degree
Celsius:

= 0.512 + 450*0.00188 = 0.512 + 0.846 = 1.358
atm