Дано:
V1 = 7 л = 7 дм³ = 0,007 м³;
V2 = 14 л = 14 дм³ = 0,014 м³;
T2 = 300 K;
p — const;
t1 — ?
Решение:
(используем закон Гей-Люссака)
V1/T1 = V2/T2,
T1 = V1*T2/V2.
T1 = 0,007*300/0,014 = 150 (K),
t1 = T1 - 273 = 150 - 273 = -123 (°C).
Ответ: -123° C.
Ответ:
ні тому що температура землі значно менша від температури нагрівання краплі
Дано:
![P = const](https://tex.z-dn.net/?f=+P+%3D+const+)
;
![V = n V_o](https://tex.z-dn.net/?f=+V+%3D+n+V_o+)
;
![n = 2.5](https://tex.z-dn.net/?f=+n+%3D+2.5+)
;
![\Delta T = 300 K](https://tex.z-dn.net/?f=+%5CDelta+T+%3D+300+K+)
.
Найти:
![T_o](https://tex.z-dn.net/?f=+T_o+)
– начальную температуру,
![T](https://tex.z-dn.net/?f=+T+)
– конечную температуру.
Решение:
Из уравнения идеального газа следует, что:
![P V_o = \nu RT_o](https://tex.z-dn.net/?f=+P+V_o+%3D+%5Cnu+RT_o+)
– формула [1] ;
![PV = \nu RT](https://tex.z-dn.net/?f=+PV+%3D+%5Cnu+RT+)
– формула [2] ;
Вычтем из формулы [2] формулу [1], отсюда:
![PV - PV_o = \nu RT - \nu RT_o](https://tex.z-dn.net/?f=+PV+-+PV_o+%3D+%5Cnu+RT+-+%5Cnu+RT_o+)
;
![P ( V - V_o ) = \nu R ( T - T_o )](https://tex.z-dn.net/?f=+P+%28+V+-+V_o+%29+%3D+%5Cnu+R+%28+T+-+T_o+%29+)
;
![P ( n V_o - V_o ) = \nu R \Delta T](https://tex.z-dn.net/?f=+P+%28+n+V_o+-+V_o+%29+%3D+%5Cnu+R+%5CDelta+T+)
;
![( n - 1 ) P V_o = \nu R \Delta T](https://tex.z-dn.net/?f=+%28+n+-+1+%29+P+V_o+%3D+%5Cnu+R+%5CDelta+T+)
– формула [3] ;
Разделим формулу [1] на формулу [3] и получим:
![\frac{ P V_o }{ ( n - 1 ) P V_o } = \frac{ \nu R T_o }{ \nu R \Delta T }](https://tex.z-dn.net/?f=+%5Cfrac%7B+P+V_o+%7D%7B+%28+n+-+1+%29+P+V_o+%7D+%3D+%5Cfrac%7B+%5Cnu+R+T_o+%7D%7B+%5Cnu+R+%5CDelta+T+%7D+)
;
![\frac{1}{ n - 1 } = \frac{T_o}{ \Delta T }](https://tex.z-dn.net/?f=+%5Cfrac%7B1%7D%7B+n+-+1+%7D+%3D+%5Cfrac%7BT_o%7D%7B+%5CDelta+T+%7D+)
;
![T_o = \frac{ \Delta T }{ n - 1 }](https://tex.z-dn.net/?f=+T_o+%3D+%5Cfrac%7B+%5CDelta+T+%7D%7B+n+-+1+%7D+)
;
![T = T_o + \Delta T = \frac{ \Delta T }{ n - 1 } + \Delta T = \Delta T ( \frac{1}{ n - 1 } + 1 ) = \Delta T \frac{ 1 + n -1 }{ n - 1 } = \Delta T \frac{n}{ n - 1 }](https://tex.z-dn.net/?f=+T+%3D+T_o+%2B+%5CDelta+T+%3D+%5Cfrac%7B+%5CDelta+T+%7D%7B+n+-+1+%7D+%2B+%5CDelta+T+%3D+%5CDelta+T+%28+%5Cfrac%7B1%7D%7B+n+-+1+%7D+%2B+1+%29+%3D+%5CDelta+T+%5Cfrac%7B+1+%2B+n+-1+%7D%7B+n+-+1+%7D+%3D+%5CDelta+T+%5Cfrac%7Bn%7D%7B+n+-+1+%7D+)
;
![T = \frac{ \Delta T }{ 1 - \frac{1}{n} }](https://tex.z-dn.net/?f=+T+%3D+%5Cfrac%7B+%5CDelta+T+%7D%7B+1+-+%5Cfrac%7B1%7D%7Bn%7D+%7D+)
;
В данном случае:
![T_o = \frac{ 300 K }{ 2.5 - 1 } = \frac{ 300 K }{1.5} = 200 K](https://tex.z-dn.net/?f=+T_o+%3D+%5Cfrac%7B+300+K+%7D%7B+2.5+-+1+%7D+%3D+%5Cfrac%7B+300+K+%7D%7B1.5%7D+%3D+200+K+)
;
![T = \frac{ 300 K }{ 1 - \frac{1}{2.5} } = \frac{ 300 K }{ 1 - \frac{2}{5} } = \frac{ 300 K }{ \frac{3}{5} } = \frac{5}{3} 300 K = 500 K](https://tex.z-dn.net/?f=+T+%3D+%5Cfrac%7B+300+K+%7D%7B+1+-+%5Cfrac%7B1%7D%7B2.5%7D+%7D+%3D+%5Cfrac%7B+300+K+%7D%7B+1+-+%5Cfrac%7B2%7D%7B5%7D+%7D+%3D+%5Cfrac%7B+300+K+%7D%7B+%5Cfrac%7B3%7D%7B5%7D+%7D+%3D+%5Cfrac%7B5%7D%7B3%7D+300+K+%3D+500+K+)
;
Ответ:
![T_o = 200 K](https://tex.z-dn.net/?f=+T_o+%3D+200+K+)
;
![T = 500 K](https://tex.z-dn.net/?f=+T+%3D+500+K+)
;