On a recent trip to the Fort Worth Zoo, Trevor's parents bought him a helium-filled balloon. At the beginning of the day, the sky was sunny and clear. The balloon was filled with 14.2 L of helium at a pressure of 102.5 kPa. The temperature was 33 °C. After a while, a storm came up, and a drop in barometric pressure and temperature reduced the pressure of the helium to 100.9 kPa and the temperature to 24 °C. What was the new volume of the balloon if there was a change? Did the volume increase or decrease?

1. The new volume is 14L

2. The volume decreased

Explanation:

Step 1:

Data obtained from the question.

Initial Volume (V1) = 14.2 L

Initial pressure (P1) = 102.5 kPa

Initial temperature (T1) = 33°C

Final pressure (P2) = 100.9 kPa

Final temperature (T2) = 24°C.

Final volume (V2) =?

Step 2:

Conversion of celsius temperature to Kelvin temperature. This is illustrated below:

K = °C + 273

T1 = 33°C = 33°C + 273 = 306K

T2 = 24°C = 24°C + 273 = 297K

Step 3:

Determination of the new volume.

Applying the general gas equation P1V1/T1 = P2V2/T2, the new volume can be obtain as follow:

P1V1/T1 = P2V2/T2

102.5 x 14.2/306 = 100.9 x V2/297

Cross multiply to express in linear form as shown below:

306 x 100.9 x V2 = 102.5 x14.2 x297

Divide both side by 306 x 100.9

V2 = (102.5x14.2x297)/(306 x 100.9)

V2 = 14 L

The new volume is 14 L.

Step 4:

Determination of the change in volume. This is illustrated below

Final volume (V2) = 14 L

Initial volume (V1) = 14.2 L

Change in volume (ΔV) =?

Change in volume (ΔV) = Final volume (V2) - Initial volume (V1)

ΔV = V2 - V1

ΔV = 14 - 14.2

ΔV = - 0.2L

Since the change in volume is negative, it means there is a decrease in the volume.

The volume decreased to 14.0 L

Explanation:

Step 1: Data given

Volume of the balloon 14.2 L

Pressure = 102.5 kPa = 1.0115963 atm

Temperature = 33 °C = 306 K

The pressure reduced to 100.9 kPa = 0.99580558

Temperature reduced = 24.0 °C = 297 K

Step 2: Calculate the new volume

(P1*V1)/T1 = (P2*V2)/T2

⇒with P1 is the initial pressure = 102.5 kPa

⇒with V1 = the initial volume of the balloon = 14.2 L

⇒with T1 = the initial temperature = 306 K

⇒with P2 = the reduced pressure = 100.9 kPa

⇒with V2 = the final volume = TO BE DETERMINED

⇒with T2 = the reduced temperature = 297 K

(102.5 kPa * 14.2 L) . 306 K  = (100.9 kPa * V2) / 297 K

4.7565 = (100.9 *V2) / 297 K

1412.68 = 100.9 * V2

V2 = 14.00 L

The volume decreased to 14.0 L

the dissolution of polymer can be thermodynamically described in 2 steps.

answer is: nuclear fusion produces elements that are heavier than helium.

nuclei combine to form a heavier nucleus, releasing energy.  

for example, fusion of hydrogen atoms at the sun.  

this fusion nuclear reaction is in the inner core of the sun and hydrogen (atomic number 1) is conveted into helium (atomic number 2).  

the inner core is the central region of the sun and all solar energy is produced in the core by nuclear fusion.