Question

Answer the following questions based on the P – T phase diagram of CO2: (a) CO2 at 1 atm pressure and temperature – 60 °C is compressed isothermally. Does it go through a liquid phase ? (b) What happens when CO2 at 4 atm pressure is cooled from room temperature at constant pressure ? (c) Describe qualitatively the changes in a given mass of solid CO2 at 10 atm pressure and temperature –65 °C as it is heated up to room temperature at constant pressure. (d) CO2 is heated to a temperature 70 °C and compressed isothermally. What changes in its properties do you expect to observe ?

Answer 1

Given: The body cools down from 80 °C to 50 °C in 5 minute, the surrounding temperature is 20 °C.

According to Newton’s law of cooling,

− dT dt =K( T- T 0 )

Where, T is the temperature of the body, T 0 is the temperature of the surrounding and K is a constant.

By integrating the above equation, we get

∫ T 1 T 2 dT K( T− T 0 ) =− ∫ t 1 t 2 dt (1)

By substituting the given values in the above equation, we get

∫ 50 80 dT K( T− T 0 ) =− ∫ 0 300 dt 1 K [ log e ( T− T 0 ) ] 50 80 =− [ t ] 0 300 2.303 K [ log 10 ( 80−20 ) ( 50−20 ) ]=−[ 300−0 ] K=−0.00231 °C/s

Now, let the temperature of the body falls down from 60 °C to 30 °C in time t.

By substituting the value in equation (1), we get

∫ T 1 T 2 dT ( −2.303 300 log 10 2 )( T− T 0 ) =− ∫ t 1 t 2 dt 1 −0.00231 °C/s ×2.303 log 10 [ T− T 0 ] 30 60 =− [ t ] 0 t 2.303× log 10 ( 60−20 30−20 )=t×( −0.00231 °C/s ) t=600 s

Thus, the temperature of the body falls down from 60 °C to 30 °C in 600 sor 10 minute.