Question

In a student experiment, a constant-volume gas thermometer is calibrated in dry ice (−78.5°C) and in boiling ethyl alcohol (78°C). The separate pressures are 0.896 atm and 1.629 atm. Hint: Use the linear relationship P = A + BT, where A and B are constants.

(a) What value of absolute zero does the calibration yield?

(b) What pressure would be found at the freezing point of water?

(c) What pressure would be found at the boiling point of water?

Answer 1

In the given case, inear relationship P = A + BT gives relation between P and T and it is in the form of y =m x+ b, which represents a straight line with slope b

Use ideal gas equation,

PV = nRT

Plot T vs P for constnt volume

Find slope,

m = (78 ) - (-78.5) / (1.629 - 0.896)

m = 213.5 °C/atm

then y-intercept:

y =m x+ b

78 = ( 213.5 °C/atm )(1.629) + b

b = -269.8 °C

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(a)

y = mx + b

y = ( 213.5 °C/atm ) ( 0 )  + ( -269.8 °C )

0 K = -269.8 °C

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(b)

y = 213.5 °C/atm (P) + ( -269.8 °C )

0 = 213.5 °C/atm (P) + ( -269.8 °C )

Solve for x

P = 1.26 atm

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(c)

y = m x+b

T = 213.5 °C/atm P   + ( -269.8 °C )

This is in the form of

y    =213.5 °C/atm P   + ( -269.8 °C )

100 = 213.5 °C/atm P   + ( -269.8 °C )​

Solve for P

P = 1.73 atm