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Hi, I'm not sure how to do the following. Could someone help me out?

Q. At sea level, where the barometric pressure is 101.3 kN/m^2 and the temperature is 20 degrees celcius, a balloon is filled with 2.5 kg of hydrogen also at 20 degrees celcius.

(i) Find the volume of the balloon at sea level.

(ii) If the balloon rises quickly to an altitude of 2000m where the barometric pressure is 80 kN/m^2 and the temperature is 2.0 degrees celcius find its volume.

(iii) If the balloon stays at 2000 m altitude until its temperature stabilises at 2 degrees celcius find its volume.

The pressure difference between the hydrogen inside the balloon and the air outside may be neglected.

My working:

(i) I just used the perfect gas equation as follows.

[tex]

V_{H_2 } = \frac{{m_{H_2 } R_{H_2 } T}}{P}

[/tex]

Is that right?

(ii) For this part I used:

[tex]

\frac{{P_1 V_1 }}{{T_1 }} = \frac{{P_2 V_2 }}{{T_2 }}

[/tex]

where the values of symbols with 1 (one) as the subscript are the same as those given or used in part (i) while P_2 = 80 kN/m^2 and T_2 = 295 K.

Solve for V_2 to find the volume of the balloon?

(iii) For this part I essentially just used [tex]\frac{{P_1 V_1 }}{{T_1 }} = \frac{{P_2 V_2 }}{{T_2 }}[/tex] again. However, this time wouldn't P_1 = P_2 = 80 kN/m^2 since the barometric pressure hasn't changed from part (ii)? Also, the temperature "stabilises at 2 degrees celcius" which is the same temperature as in part (ii). But this seems to imply that the required volume is just the same as that found in part (ii).

I'm not really sure what to do here. Can someone check my working and point me in the right direction? Thanks.

Q. At sea level, where the barometric pressure is 101.3 kN/m^2 and the temperature is 20 degrees celcius, a balloon is filled with 2.5 kg of hydrogen also at 20 degrees celcius.

(i) Find the volume of the balloon at sea level.

(ii) If the balloon rises quickly to an altitude of 2000m where the barometric pressure is 80 kN/m^2 and the temperature is 2.0 degrees celcius find its volume.

(iii) If the balloon stays at 2000 m altitude until its temperature stabilises at 2 degrees celcius find its volume.

The pressure difference between the hydrogen inside the balloon and the air outside may be neglected.

My working:

(i) I just used the perfect gas equation as follows.

[tex]

V_{H_2 } = \frac{{m_{H_2 } R_{H_2 } T}}{P}

[/tex]

Is that right?

(ii) For this part I used:

[tex]

\frac{{P_1 V_1 }}{{T_1 }} = \frac{{P_2 V_2 }}{{T_2 }}

[/tex]

where the values of symbols with 1 (one) as the subscript are the same as those given or used in part (i) while P_2 = 80 kN/m^2 and T_2 = 295 K.

Solve for V_2 to find the volume of the balloon?

(iii) For this part I essentially just used [tex]\frac{{P_1 V_1 }}{{T_1 }} = \frac{{P_2 V_2 }}{{T_2 }}[/tex] again. However, this time wouldn't P_1 = P_2 = 80 kN/m^2 since the barometric pressure hasn't changed from part (ii)? Also, the temperature "stabilises at 2 degrees celcius" which is the same temperature as in part (ii). But this seems to imply that the required volume is just the same as that found in part (ii).

I'm not really sure what to do here. Can someone check my working and point me in the right direction? Thanks.

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