Problem Page
The volume V of a fixed amount of a gas varies directly as the temperature T and inversely as the pressure P. Suppose that V=42 cm to the 3,when T=84 kelvin and
P= 8kg over cm squared. Find the temperature when
V=74 cm cubed and
P= 10 kg over cm squared.
To find the temperature when V = 74 cm³ and P = 10 kg/cm², we will use the formula that relates the volume, temperature, and pressure:
V ∝ T/P
First, let's solve for the constant of proportionality (k) using the given values of V = 42 cm³, T = 84 K, and P = 8 kg/cm².
42 = k * (84/8)
42 = k * 10.5
Divide both sides of the equation by 10.5 to isolate k:
k = 42 / 10.5
k = 4
Now, we can use the value of k to find the temperature (T) when V = 74 cm³ and P = 10 kg/cm².
74 = 4 * (T/10)
Divide both sides by 4 to solve for T:
T/10 = 74/4
T/10 = 18.5
Multiply both sides by 10 to isolate T:
T = 18.5 * 10
T = 185
Therefore, the temperature when V = 74 cm³ and P = 10 kg/cm² is 185 K.
We are given that the volume V varies directly with the temperature T and inversely with the pressure P.
Let's denote the constant of proportionality as k.
From the given information, we have the following equation:
V = k * (T / P)
To find the value of k, we can substitute the given values into the equation and solve for k.
42 = k * (84 / 8)
Simplifying the equation, we get:
42 = 10.5k
Dividing both sides by 10.5, we find:
k = 4
Now that we have the value of k, we can use it to find the temperature T when V = 74 cm³ and P = 10 kg over cm².
74 = 4 * (T / 10)
Simplifying the equation, we get:
74 = (2T) / 5
Multiplying both sides by 5, we find:
370 = 2T
Dividing both sides by 2, we find:
T = 185 Kelvin
Therefore, when V = 74 cm³ and P = 10 kg over cm², the temperature T is 185 Kelvin.
V=kT/P so PV/T = k, a constant. You want T such that
10*74/T = 8*42/84
also, "cm to the 3" is written cm^3