For 1 mol of a gas, the Ideal Gas Law can be stated in the following form, For 1

Question

For 1 mol of a gas, the Ideal Gas Law can be stated in the following form,

For 1 mol of a gas, the Ideal Gas Law can be stated in the following form, which expresses pressure, P, as a function of volume, V, and temperature, T. P(V, T) = 8.314T/V In this formula, the units of pressure are Pascals, the units of temperature are degrees Kelvin, and the units of volume are cubic meters. Calculate P_v (20, 300) and explain what this number means in terms of the relationship between pressure, volume, and temperature. Suppose that volume and temperature are both changing in such a way that when the volume increases by 1 cubic meter, the temperature increases by 2 degrees Kelvin. Under these circumstances, find the instantaneous rate of change of pressure when the volume is 20 cubic meters and the temperature is 300 degrees Kelvin. The graph of P(V, T) = 8.314T/V is a surface in three-dimensional space. Find a of parametric equations for the tangent line to this surface in the "V direction" at the point on the surface corresponding to (20, 300).

Explanation / Answer

PV(20,300) means here volume = 20 m3 and Temperature is 300 K,

P = 8.314 * 300/20 = 124.71 Pa

Here dV = 1 and dT = -2

dP = 8.314 (V*dT - TdV / V^2)

= 8.314(20*(-2)-300*(1))/(400)

= -7.0

Instantaneous pressure = P + dP = 124.7-7.0 = 117.7 Pa

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.