Question

(a) Translate the following into a mathematical statement: “For an ideal gas at constant pressure, it is known that the volume of the gas V, is directly proportional to the temperature of the gas T (in Kelvin).

(b) If a certain gas has a volume of 1.8 cubic meters at a temperature of 225 Kelvin, find the constant k and write the mathematical model that relates the V and K.

(c) Use your model from (b) to find the temperature of the gas if the volume increases to 2.6 cubic meters. Show all work​

Answer 1

Answer:

Given

v \times {t}^{2}v×t

2

x means proportional..

Let's assume the constant to be C...

v = c {t}^{2}v=ct

2

Given relation

v=1.8m³

Temp- 225k

1.8 = {15}^{2} k1.8=15

2

k

\frac{0.2}{25} = \frac{2}{250} = \frac{1}{125} = 0.008

25

0.2

=

250

2

=

125

1

=0.008

Now V increased = 2.6-1.8m³=0.8m³

c=0.008

So

0.8 = 0.008( {t}^{2} )0.8=0.008(t

2

)

t = 10t=10

Now temperature of gas is (225+10)K.... 235k